(square roots of the identity matrix) For how many
(square roots of the identity matrix) For how many
Step 1
To find how many matricec A of order 2 exists such that
Here we have to find
Let us consider any arbitrary matrix of order 2.
Then
Now from
Step 2
Case 1:
If
From (3) we get :
From (4) we get :
From (1) we get :
From (2) we get :
Therefore we get the matrix of the form
Step 3
Case 2:
If
sub case a:
If a=0 , that implies
Then from(1 ) and (2) , we get :
Therefore we get the matrix of the form
Step 4
We can also consider further subcases to find the type of involuntary matrices, but as the question is asked to find how many, we have already got infinitely many
Similarly for any
Answer is given below (on video)
Answer is given below (on video)